LowTFMuonium

Description

A relaxation function for a pair of transver field triplet muonium frequencies.

A(t)=A04{(1+δ)a12cos(ω12+ϕ)+(1δ)a23cos(ω23+ϕ)}

and,

δ=χ1+χ2,
χ=(gμ+ge)BA,
d=(gegμ)ge+gμ,
E1=A4(1+2dχ),
E2=A4(1+21+χ2),
E3=A4(12dχ),
ωij=2π(EiEj),
aij=1(1+(ωij/(2πfcut))2),

where,

A0 is the amplitude,

A (MHz) is the isotropic hyperfine coupling constant,

ϕ (rad) is the phase at time t=0,

gμ=0.01355342 , the gyromagnetic ratio of muon,

ge=2.8024 , the gyromagnetic ratio of electron,

and fcut=1032 (MHz).

(Source code, png, hires.png, pdf)

../../_images/LowTFMuonium-1.png

Properties (fitting parameters)

Name

Default

Description

A0

0.2

Amplitude

Field

0.1

Magnetic Field (G)

A

0.2

Isotropic hyperfine coupling constant (MHz)

Phi

0.0

Phase (rad)

References

[1] P. Percival, TRIUMF Summer Institute 2011.

[2] F.L. Pratt, Physica B 289-290, 710 (2000).

Categories: FitFunctions | Muon\MuonSpecific

Source

Python: LowTFMuonium.py